This is just a simple yes or no question whether $xy=0$ can be considered as a rectangular hyperbola or not.
I was doing a sum where it said the following :
If the straight line $3x + 4y = 24$ meets the axes at $A$ and $B$ and the line $4x + 3y = 24$ meets the axes at $C$ and $D$, then show that the points lie on a conic section which has to be an ellipse.
Well, I then thought that it lies on $xy=0.$
So is $xy=0$ a conic ?
Yes... A pair of straight lines obtained by cutting a right circular cone through its apex. It is a degenerate conic with a sharp slope change at the origin. The combination curve of the x-y- axes.
Special case when in hyperbola set $ x\cdot y=c^2, c=0.$